First Course in Differential Equations : With Modeling Applications
ISBN: 9780495108245 | 0495108243
Edition: 9thFormat: Hardcover
Publisher: Brooks Cole
Pub. Date: 5/14/2008
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A First Course in Differential Equations with Modeling Applications, 9th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and p... MORE
| Introduction to Differential Equations | |
| Definitions and Terminology | |
| Initial-Value Problems | |
| Differential Equations as Mathematical Models | |
| Chapter 1 in Review | |
| First-Order Differential Equations | |
| Solution Curves Without a Solution | |
| Separable Variables | |
| Linear Equations | |
| Exact Equations and Integrating Factor... MORE | |
| Solutions by Substitutions | |
| A Numerical Method | |
| Chapter 2 in Review | |
| Modeling with First-Order Differential Equations | |
| Linear Models | |
| Nonlinear Models | |
| Modeling with Systems of First-Order Differential Equations | |
| Chapter 3 in Review | |
| Higher-Order Differential Equations | |
| Preliminary Theory- Linear Equations | |
| Reduction of Order | |
| Homogeneous Linear Equations with Constant Coefficients | |
| Undetermined Coefficients- Superposition Approach | |
| Undetermined Coefficients- Annihilator Approach | |
| Variation of Parameters | |
| Cauchy-Euler Equation | |
| Solving Systems of Linear Differential Equations by Elimination | |
| Nonlinear Differential Equations | |
| Chapter 4 in Review | |
| Modeling with Higher-Order Differential Equations | |
| Linear Models: Initial-Value Problems | |
| Linear Models: Boundary-Value Problems | |
| Nonlinear Models | |
| Chapter 5 in Review | |
| Series Solutions of Linear Equations | |
| Solutions About Ordinary Points | |
| Solutions About Singular Points | |
| Special Functions | |
| Chapter 6 in Review | |
| Laplace Transform | |
| Definition of the Laplace Transform | |
| Inverse Transform and Transforms of Derivatives | |
| Operational Properties I | |
| Operational Properties II | |
| Dirac Delta Function | |
| Systems of Linear Differential Equations | |
| Chapter 7 in Review | |
| Systems of Linear First-Order Differential Equations | |
| Preliminary Theory | |
| Homogeneous Linear Systems | |
| Nonhomogeneous Linear Systems | |
| Matrix Exponential | |
| Chapter 8 in Review | |
| Numerical Solutions of Ordinary Differential Equations | |
| Euler Methods | |
| Runge-Kutta Methods | |
| Multistep Methods | |
| Higher-Order Equations and Systems | |
| Second-Order Boundary-Value Problems | |
| Chapter 9 in Review | |
| Gamma Function | |
| Matrices | |
| Laplace Transforms | |
| Answers for Selected Odd-Numbered Problems | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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